Why do the thought police allow Julia and Winston to carry on their relationship as long as they do?Since the screen in their room was presumably...

Sometimes, you have to give people enough rope in order that they will hang themselves with it.

In the instance of Winston and Julia, the affair was probably not a secret as they hoped, but the trap was set probably to catch Julia more than to catch Winston. He was just an innocent victim in the plot to entrap Julia.

From the beginning of the book, Winston appears to be compliant but somewhat dissatisfied with the whole social order. It is not until he meets Julia, falls in love with her and begins an affair that he realizes that he does not love Big Brother as a good party member ought to.